The Klein model

The Klein model, also known as the Klein disk, is a way to represent geometric spaces called hyperbolic geometry within a circle. Imagine drawing a circle and placing points inside it to represent a special kind of space where parallel lines can diverge. In this model, straight lines are represented as chords or line segments within the circle, and the entire hyperbolic space fits inside the boundary, which acts as a horizon. The Klein model allows us to visualize and analyze hyperbolic geometry using familiar Euclidean tools, making complex non-Euclidean concepts more accessible.